Core Logic
We work backwards. Both (Q) and (R) give a positive iodoform test (yellow precipitate with NaOI). Since (Q) and (R) are obtained by treating alkyl iodides with aq. NaOH, they must be alcohols.
Alcohols that give a positive iodoform test must possess the structural unit CH₃-CH(OH)-$CH_3-CH(OH)-$. Therefore, both alkyl iodides must contain the CH₃-CH(I)-$CH_3-CH(I)-$ group.
The precursor mixed ether (P) was treated with excess concentrated HI to yield these two alkyl iodides. For both sides of the ether to produce iodides capable of forming secondary alcohols with terminal methyls upon hydrolysis, the ether must be composed of two branches that look like -CH(CH₃)-$-CH(CH_3)-$.
Let's evaluate the correct option (1):
Structure (P) is an ether linking a sec-butyl group and a secondary-pentyl group (or similar structure). Excess HI cleaves the ether to give two secondary alkyl iodides.
Hydrolysis with aq. NaOH converts both alkyl iodides into secondary alcohols.
Both secondary alcohols have a methyl group directly adjacent to the hydroxyl-bearing carbon, fully satisfying the iodoform test requirement.
Pattern Recognition
Excess hot HI cleaves ethers (R-O-R'$R-O-R'$) into two moles of alkyl iodides (R-I$R-I$ and R'-I$R'-I$). Only secondary alcohols with a methyl group or ethanol itself give positive iodoform tests. Look for an ether containing CH₃-CH(O-)-$CH_3-CH(O-)-$ branching on BOTH sides.
Chapter Mix
Class 12 Chemistry: Alcohols, Phenols and Ethers
Class 12 Chemistry: Haloalkanes and Haloarenes
Class 12 Chemistry: Aldehydes, Ketones and Carboxylic Acids